Home
Class 12
MATHS
The number of intergal values of x if 5x...

The number of intergal values of x if `5x -1 lt (x+1)^2 lt 7 x-3 ` is

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
B
We have` (x+1)^2 lt 5x -1`
`rArr x^2-3x +2 lt 0 `
`rArr (x-1)(x-2)lt0 `
`rArr x lt 1 or x gt 2`
And `(x+1)^2 le 7x -3`
`x^2- 5x +4 lt 0 `
`rArr (x-1)(x-4) lt 0 `
`1 lt x lt 4 `
From (i) and (ii) common values are `x in (2,4)`
Therefore , there is only one integral value of x which is 3
Promotional Banner

Topper's Solved these Questions

  • SET THEORY AND REAL NUMBER SYSTEM

    CENGAGE|Exercise Archieves|1 Videos

  • SET THEORY AND REAL NUMBER SYSTEM

    CENGAGE|Exercise Exercise 1.5|12 Videos

  • SEQUENCE AND SERIES

    CENGAGE|Exercise Question Bank|36 Videos

  • SETS AND RELATIONS

    CENGAGE|Exercise Question Bank|15 Videos

Similar Questions

Explore conceptually related problems

Solution set of (5x-1)lt (x+1)^(2)lt (7x -3) is

Number of intergal values of x satisfying the inequality (x^2+6x-7)/(|x+2||x+3|) lt 0 is

For 2 lt x lt 4 find the values of |x|. (ii) For -3 le x le -1 , find the values of |x|. (iii) For -3 le x lt 1, find the values of |x| (iv) For -5 lt x lt 7 find the values of |x-2| (v) For 1 le x le 5 find fthe values of |2x -7|

Find the number of integral solutions of x_1+x_2+x_3+=24 subjected to the condition that 1lt=x_1lt=5,12lt=x_2lt=18 and -1lt=x_3

The set of all values of x for which ((x+1)(x-3)^(2)(x-5)(x-4)^(3)(x-2))/(x) lt 0

Find the range of values of x which satisfy the inequlaity - 1/5lt (3x)/10 + 1lt 2/5,x epsilon R .

If the median of the scores 1, 2, x, 4 and 5 (where 1 lt 2 lt x lt 4 lt 5 ) is 3, then the mean of the scores is ______.

CENGAGE-SET THEORY AND REAL NUMBER SYSTEM -Exercises
  1. Which is the simplified representation of (A' cap B' cap C) cup (B cap...

    Text Solution

    |

  2. In statistical survey of 1003 families has neither a radio nor a TV, 7...

    Text Solution

    |

  3. A survey shows that 63 % of the pepole watch a news channel whereas , ...

    Text Solution

    |

  4. In a town of 10,000 families it was found that 40% family buy newspape...

    Text Solution

    |

  5. Complete solution set of inequlaity ((x+2)(x+3))/((x-2)(x-3))le1

    Text Solution

    |

  6. The number of intergal values of x if 5x -1 lt (x+1)^2 lt 7 x-3 is

    Text Solution

    |

  7. If set A ={x|(x^2(x-5)(2x-1))/((5x+1)(x+2)) lt 0 } and Set B={x|(3x...

    Text Solution

    |

  8. Number of intergers satisfying the inequality x^4- 29x^2+100 le 0 i...

    Text Solution

    |

  9. If n gt 0 and exactly 15 integers satisfying (x+6)(x-4 ) (x-5) (2x-...

    Text Solution

    |

  10. The solution of the inequality ((x+7)/(x-5)+(3x+1)/(2) ge 0 is

    Text Solution

    |

  11. The complete solution set of inequality ((x-5)^(1005)(x+8)^(1008)(x-1)...

    Text Solution

    |

  12. Sum of solution of the equation |x|^3-4|x|^2+3|x|=0 is

    Text Solution

    |

  13. Number of intergral roots of |x-1||x^2-2|=2 is

    Text Solution

    |

  14. The solution set of the inequlity (|x-2|-x)/(x)lt2 is

    Text Solution

    |

  15. Number of solutions of the equation |2-|x||=x +4 is

    Text Solution

    |

  16. Number of intergal values of x satisfying the inequality (x^2+6x-7)/(|...

    Text Solution

    |

  17. If -4lex lt 2 then ||x+2|-3 lies in the inerval

    Text Solution

    |

  18. Complete set of values of x satisfying inequality ||x-1|-5| lt 2x -5 ...

    Text Solution

    |

  19. If |x^2-2x+2|-|2x^2-5x+2|=|x^2-3x| then the set of values of x is

    Text Solution

    |

  20. The complete solution set of the equation |x^2-5x+6|+|x^2+12x+27|=17x ...

    Text Solution

    |